Normal forms of matrices over the ring of formal series

TL;DR

This paper studies matrices over formal power series rings and constructs their normal forms under various transformations, utilizing a filtration induced by the action on polynomial maps.

Contribution

It introduces a method to derive normal forms of matrices over formal series rings using a filtration approach based on polynomial map subspaces.

Findings

Normal forms are constructed for matrices over formal power series rings.

The approach leverages a filtration induced by the action on polynomial maps.

The method applies to various sub-group transformations.

Abstract

Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a filtration by projectors on sub-spaces of polynomial maps.